Recently, it was argued (Eur. Phys. J. C {\bf73}, 2487 (2013)) that the totalentropy of a gravitational system should be related to the volume of systeminstead of the system surface. Here, we show that this new proposal cannotsatisfy the unified first law of thermodynamics and the Friedmans equationsimultaneously, unless the effects of dark energy candidate on the horizonentropy are considered. In fact, our study shows that some types of dark energycandidate may admit this proposal. Some general properties of required darkenergy are also addressed. Moreover, our investigation shows that this newproposal for entropy, while combined with the second law of thermodynamics (asthe backbone of Verlinde's proposal), helps us in providing a thermodynamicinterpretation for the difference between the surface and bulk degrees offreedom which, according to Padmanabhan's proposal, leads to the emergence ofspacetime and thus the universe expansion. In fact, our investigation showsthat the entropy changes of system may be equal to the difference between thesurface and bulk degrees of freedom falling from surface into the systemvolume. Briefly, our results signal us that this new proposal for entropy maybe in agreement with the thermodynamics laws, the Friedmann equation,Padmanabhan's holographic proposal for the emergence of spacetime and thereforethe universe expansion. In fact, this new definition of entropy may be used tomake a bridge between Verlinde's and Padmanabhan's proposals.
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机译：最近，有人争论（Eur。Phys。J. C {\ bf73}，2487（2013）），引力系统的总熵应该与系统的体积而不是系统表面有关。在这里，我们表明，除非考虑了暗能量候选物对水平熵的影响，否则该新提议不能同时满足热力学统一的第一定律和弗里德曼方程。实际上，我们的研究表明，某些类型的暗能量候选对象可能会接受该建议。还讨论了所需暗能量的一些常规属性。此外，我们的研究表明，这种新的熵提案与热力学第二定律（作为Verlinde提议的主旨）相结合，有助于我们对表面自由度和体积自由度之间的差异提供热力学解释，根据Padmanabhan的提议，导致时空的出现，从而宇宙膨胀。实际上，我们的研究表明，系统的熵变可能等于从表面进入系统体积的表面自由度与体自由度之差。简而言之，我们的结果表明，关于熵的这一新提议可能与热力学定律，弗里德曼方程，帕德曼纳罕关于时空的出现以及因此宇宙膨胀的全息提议相吻合。实际上，这种新的熵定义可以用来在Verlinde和Padmanabhan的建议之间架起一座桥梁。
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